Decomposable Graphs and Hypergraphs

Abstract

We define and investigate the notion of a decomposable hypergraph, showing that such a hypergraph always is conformal, that is, can be viewed as the class of maximal cliques of a graph. We further show that the clique hypergraph of a graph is decomposable if and only if the graph is triangulated and characterise such graphs in terms of a combinatorial identity. © 1984, Australian Mathematical Society. All rights reserved.